A concept of a high-power magnetron transmitter utilizing the vector addition of signals of Continuous Wave (CW) magnetrons, injection-locked by phase-modulated signals, and intended to operate within a wideband control feedback loop in phase and amplitude, is presented. This transmitter is proposed to drive Superconducting RF (SRF) cavities for intensity-frontier GeV-scale proton/ion linacs, including linacs for Accelerator Driven System (ADS). The transmitter performance was verified in experiments with CW, S-Band, 1 kW magnetrons. A wideband dynamic control of magnetrons, required for the superconducting linacs, was realized using the magnetrons, injectionlocked by the phase-modulated signals. The capabilities of the magnetrons injection-locked by the phase-modulated signals and adequateness for feeding of SRF cavities have been verified by measurements of the transfer function magnitude characteristics of single and 2-cascade magnetrons in the phase modulation domain, by measurements of the magnetrons phase performance and by measurements of spectra of the carrier frequency of the magnetrons. At the ratio of power of locking signal to output power of ≥ -13 dB (in 2-cascade scheme per magnetron, respectively) we demonstrated a phase modulation bandwidth of over 1.0 MHz for injection-locked CW single magnetrons and a 2-cascade setup, respectively. The carrier frequency spectrum (width of ~ 1 Hz at the level of <-60 dBc) of the magnetron, injection-locked by a phase-modulated signal, did not demonstrate broadening at wide range of magnitude and frequency of the phase modulation. The wideband dynamic control of output power of the transmitter model has been first experimentally demonstrated using two CW magnetrons, combined in power and injection-locked by the phasemodulated signals. The experiments with the injection-locked magnetrons adequately emulated the wideband dynamic control with a feedback control system, which will allow to suppress parasitic modulation of the accelerating field in the SRF cavities, resulted from mechanical noises, phase perturbations, caused by cavity beam loading and cavity dynamic tuning errors, low-frequency ripples of the magnetron power supplies, etc. The magnetron transmitter concept, tests of the transmitter models and injection-locking of magnetrons by phase-modulated signals are discussed in this work.